Question

Jack is twice the age of Lacy. After three years, the sum of their ages will be $54$.Find the present ages of Jack and Lacy.

Answer 1

Hint: Jack’s age is two times the age of Lacy and after three years, Jack gets $3$ year older and Lacy also become $3$ year older from their present ages and the sum of the age of Jack and Lacy after three years is given i.e. $54$ and we have to find the present age of Jack and Lacy.

Complete step by step answer:
Let us assume that the present age of Lacy is $x$ and Jack is twice the age of Lacy. So the present age of Jack is $2x$.To find the age of Lacy and Jack after three years, we need to add the number of years $(3)$ in their present ages. After three years,
Age of Lacy$ = x + 3$ and, Age of Jack$ = 2x + 3$
The sum of the ages of Lacy and Jack, after three years is $54$.
Age of Lacy after three years $ + $ age of Jack after three years$ = 54$
After substituting, we get,
$(x + 3) + (2x + 3) = 54 \\
\Rightarrow x + 3 + 2x + 3 = 54 \\
\Rightarrow 3x + 6 = 54 \\
\Rightarrow 3x = 54 - 6 \\
\Rightarrow 3x = 48 \\
\Rightarrow x = \dfrac{{48}}{3} \\
\therefore x = 16 \\ $
So, the present age of Lacy is $16$ years and the present age of Jack is $2x = 2 \times 16 = 32$ years.

Note:We can also check our answer as the age of Lacy after three years will become $16 + 3 = 19$ years and the age of Jack after three years will become $32 + 3 = 35$ years and the sum of their ages after three years is $54$. So, if we add the ages of Lacy and Jack $(19 + 35 = 54)$, the sum is $54$.Hence, proved that the answer is correct.